Spectral enclosures and complex resonances for general self-adjoint operators

Abstract: This paper considers a number of related problems concerning the computation of eigenvalues and complex resonances of a general self-adjoint operator H when one is provided with limited information about the operator. The feature which ties the different sections together is that one restricts oneself to spectral properties of H which can be proved by using only vectors from a pre-assigned (possibly finite-dimensional) linear subspace L which is not invariant with respect to the operator. Problems of this type arise in numerical analysis and quantum chemistry (and probably elsewhere).